Analytics and algorithms for geometric average trigger reset options

Tian-Shyr Dai, I. Yuan Chen, Yuh Yuan Fang, Yuh Dauh Lyuu

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

The geometric average trigger reset option resets the strike price based on the geometric average of the underlying asset's prices over a monitoring window. This paper derives an analytic formula and two numerical methods for pricing this option with multiple resets. The analytic formula in fact is a corollary of a general formula that holds for a large class of path-dependent options: It prices any option whose payoff function can be written as eb-X1{XεA}. For general American-style reset options, an O(n4h2-time algorithm on n-period binomial lattice is presented. A much more efficient O(n3hm)-time algorithm prices European-style reset options. Monte Carlo simulation suggests that the European-style geometric average trigger reset option and the arithmetic version have similar option values. This implies that results in this paper give tight prices for the difficult arithmetic version.

Original languageEnglish
Title of host publication2003 IEEE International Conference on Computational Intelligence for Financial Engineering, CIFEr 2003 - Proceedings
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages55-62
Number of pages8
ISBN (Electronic)0780376544
DOIs
StatePublished - 1 Jan 2003
Event2003 IEEE International Conference on Computational Intelligence for Financial Engineering, CIFEr 2003 - Hong Kong, China
Duration: 20 Mar 200323 Mar 2003

Publication series

NameIEEE/IAFE Conference on Computational Intelligence for Financial Engineering, Proceedings (CIFEr)
Volume2003-January

Conference

Conference2003 IEEE International Conference on Computational Intelligence for Financial Engineering, CIFEr 2003
CountryChina
CityHong Kong
Period20/03/0323/03/03

Keywords

  • Algorithm design and analysis
  • Arithmetic
  • Computer science
  • Computerized monitoring
  • Finance
  • Investments
  • Lattices
  • Monte Carlo methods
  • Pricing
  • Protection

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  • Cite this

    Dai, T-S., Chen, I. Y., Fang, Y. Y., & Lyuu, Y. D. (2003). Analytics and algorithms for geometric average trigger reset options. In 2003 IEEE International Conference on Computational Intelligence for Financial Engineering, CIFEr 2003 - Proceedings (pp. 55-62). [1196242] (IEEE/IAFE Conference on Computational Intelligence for Financial Engineering, Proceedings (CIFEr); Vol. 2003-January). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CIFER.2003.1196242